HyperVis: Continuous Latent Visual Relational Graphs on the Lorentz Hyperboloid for Compositional Reasoning

Vision-Language Models (VLMs) struggle with compositional reasoning that requires understanding inter-object relationships. A natural remedy is to inject explicit scene graph triplets langle s, p, o rangle from an off-the-shelf scene graph generator (SGG), but we show this backfires: discrete text labels collide with the continuous visual modality, degrading GQA accuracy from 60.38% to 58.86%. We propose HyperVis, which bypasses the SGG semantic bottleneck entirely. From N class-agnostic region proposals, we compute a dense O(N2) visual relation tensor via spatially-biased cross-attention, project it onto a Lorentz hyperboloid, and enforce hierarchy through spatial physics, namely IoA-driven entailment cones and exterior-angle repulsion. We discover that HyperVis contributes in two complementary ways: (1) as a training-time regularizer, the hyperbolic relational losses shape LoRA representations that improve generative VQA (GQA 61.03% vs. 57.21% for LoRA fine-tuning without relational losses, recovering and surpassing the baseline); and (2) as an inference-time relational encoder, hyperbolic prefix tokens boost discriminative compositional scoring (SugarCrepe 79.94%, +6.25pp over baseline). The learned curvature stabilises at kappa=4.0, an order of magnitude above prior hyperbolic VLMs where kappa typically collapses toward zero, indicating that continuous visual features genuinely require the exponential volume of strongly curved space. A controlled Euclidean ablation confirms this decomposition: the relational pipeline regularises LoRA comparably in flat space (GQA 60.81%), but the compositionality gain is specifically hyperbolic (SugarCrepe +4.58pp over Euclidean), with entailment loss ~6× higher in Euclidean training. Codes are available at TBA.